6
• ( , V
The solution of the equation is X k = b (b<l).
The steady state distribution of the population according
ir t • • • • Tr
to rank is (l-b)b and the tail of the distribution is b .
The steady state solution in Champernowne's case is thus
equivalent to the simplified case treated further above,
if p is replaced by b.
The aim of the preceding considerations is to show that
Champernowne's explanation of the Pareto law is basically
the same as that of Simon (1957)and myself (1965) which
goes back to the model of Yule (1924) who used it to
explain the frequency of species in genera. 2 According to
this approach size distribution is a transformed age
distribution and the pattern of the Pareto law occurs so
often simply because of the empirical importance of
exponential growth which makes both the age distribution
and the transformation function exponential. Owing to the
conceptual density of Champernowne's model the two
elements of rank in the hierarchy and income as a function
of rank are merged into one.
There is,however, a difference (which relates to the
interpretation rather than to the form ) between
Champernowne's model and the others:Since physical persons
sooner or later die the age or rank in his model is
limited while in other models, of firms or of wealth,for